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Entropy-bounded solutions to the Cauchy problem of compressible heat-conducting magnetohydrodynamic equations with far field vacuum

主讲人：钟新

摘要：In this talk, we will investigate the Cauchy problem to compressible heat-conducting magnetohydrodynamic equations with vacuum at infinity only. We show that the uniform boundedness of the entropy and the  regularities of the velocity and temperature can be propagated provided that the initial density decays suitably slow at infinity. The main tools are based on singularly weighted energy estimates and De Giorgi type iteration techniques developed by Li and Xin (Adv. Math., 361 2020; Comm. Pure Appl. Math., 2022; https://arxiv.org/abs/2111.14057) for the full compressible Navier-Stokes system. Some new mathematical techniques and useful estimates are developed to deduce the lower and upper bounds on the entropy.

主讲人简介：钟新，西南大学数学与统计学院教授，数学系主任，主要研究兴趣为流体方程组解的整体适定性和奇点的形成，部分研究成果发表在 J. Math. Pures Appl.、Indiana Univ. Math. J.、Calc. Var. Partial Differential Equations、Nonlinearity、J. Math. Fluid Mech.、J. Differential Equations 等期刊上。主持国家自然科学基金、中国博士后科学基金、重庆市自然科学基金等国家级和省部级科研项目8项。

邀请人：雷远杰

时间：：2022年7月13日 （星期三）13: 00-14:30

地点：腾讯会议室     ID:736 682 488